LMFDB - Embedded newform 6422.2.a.bn.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.58539$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.58539 q^{3} +1.00000 q^{4} +2.09051 q^{5} +1.58539 q^{6} +3.27454 q^{7} +1.00000 q^{8} -0.486543 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.58539 q^{3} +1.00000 q^{4} +2.09051 q^{5} +1.58539 q^{6} +3.27454 q^{7} +1.00000 q^{8} -0.486543 q^{9} +2.09051 q^{10} -0.186969 q^{11} +1.58539 q^{12} +3.27454 q^{14} +3.31427 q^{15} +1.00000 q^{16} +2.82867 q^{17} -0.486543 q^{18} +1.00000 q^{19} +2.09051 q^{20} +5.19141 q^{21} -0.186969 q^{22} -1.53315 q^{23} +1.58539 q^{24} -0.629758 q^{25} -5.52753 q^{27} +3.27454 q^{28} +5.03671 q^{29} +3.31427 q^{30} +4.59919 q^{31} +1.00000 q^{32} -0.296419 q^{33} +2.82867 q^{34} +6.84546 q^{35} -0.486543 q^{36} -2.06596 q^{37} +1.00000 q^{38} +2.09051 q^{40} +3.56501 q^{41} +5.19141 q^{42} -7.69760 q^{43} -0.186969 q^{44} -1.01713 q^{45} -1.53315 q^{46} +5.47953 q^{47} +1.58539 q^{48} +3.72260 q^{49} -0.629758 q^{50} +4.48454 q^{51} +1.39814 q^{53} -5.52753 q^{54} -0.390862 q^{55} +3.27454 q^{56} +1.58539 q^{57} +5.03671 q^{58} -1.94161 q^{59} +3.31427 q^{60} +8.31755 q^{61} +4.59919 q^{62} -1.59320 q^{63} +1.00000 q^{64} -0.296419 q^{66} -1.17201 q^{67} +2.82867 q^{68} -2.43063 q^{69} +6.84546 q^{70} +3.09652 q^{71} -0.486543 q^{72} -11.9094 q^{73} -2.06596 q^{74} -0.998411 q^{75} +1.00000 q^{76} -0.612238 q^{77} -2.06190 q^{79} +2.09051 q^{80} -7.30364 q^{81} +3.56501 q^{82} +13.1907 q^{83} +5.19141 q^{84} +5.91337 q^{85} -7.69760 q^{86} +7.98514 q^{87} -0.186969 q^{88} -9.20255 q^{89} -1.01713 q^{90} -1.53315 q^{92} +7.29151 q^{93} +5.47953 q^{94} +2.09051 q^{95} +1.58539 q^{96} -0.735611 q^{97} +3.72260 q^{98} +0.0909688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.58539	0.915324	0.457662	−	0.889126i	$-0.348687\pi$
$3$	1.58539	0.915324	0.457662	+	0.889126i	$0.348687\pi$
$4$	1.00000	0.500000
$5$	2.09051	0.934906	0.467453	−	0.884018i	$-0.345172\pi$
$5$	2.09051	0.934906	0.467453	+	0.884018i	$0.345172\pi$
$6$	1.58539	0.647232
$7$	3.27454	1.23766	0.618829	−	0.785525i	$-0.287607\pi$
$7$	3.27454	1.23766	0.618829	+	0.785525i	$0.287607\pi$
$8$	1.00000	0.353553
$9$	−0.486543	−0.162181
$10$	2.09051	0.661078
$11$	−0.186969	−0.0563734	−0.0281867	−	0.999603i	$-0.508973\pi$
$11$	−0.186969	−0.0563734	−0.0281867	+	0.999603i	$0.508973\pi$
$12$	1.58539	0.457662
$13$	0	0
$13$	0	0
$14$	3.27454	0.875157
$15$	3.31427	0.855742
$16$	1.00000	0.250000
$17$	2.82867	0.686053	0.343027	−	0.939326i	$-0.388548\pi$
$17$	2.82867	0.686053	0.343027	+	0.939326i	$0.388548\pi$
$18$	−0.486543	−0.114679
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.09051	0.467453
$21$	5.19141	1.13286
$22$	−0.186969	−0.0398620
$23$	−1.53315	−0.319683	−0.159842	−	0.987143i	$-0.551098\pi$
$23$	−1.53315	−0.319683	−0.159842	+	0.987143i	$0.551098\pi$
$24$	1.58539	0.323616
$25$	−0.629758	−0.125952
$26$	0	0
$27$	−5.52753	−1.06377
$28$	3.27454	0.618829
$29$	5.03671	0.935294	0.467647	−	0.883915i	$-0.345102\pi$
$29$	5.03671	0.935294	0.467647	+	0.883915i	$0.345102\pi$
$30$	3.31427	0.605101
$31$	4.59919	0.826039	0.413020	−	0.910722i	$-0.364474\pi$
$31$	4.59919	0.826039	0.413020	+	0.910722i	$0.364474\pi$
$32$	1.00000	0.176777
$33$	−0.296419	−0.0516000
$34$	2.82867	0.485113
$35$	6.84546	1.15709
$36$	−0.486543	−0.0810906
$37$	−2.06596	−0.339642	−0.169821	−	0.985475i	$-0.554319\pi$
$37$	−2.06596	−0.339642	−0.169821	+	0.985475i	$0.554319\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	2.09051	0.330539
$41$	3.56501	0.556761	0.278380	−	0.960471i	$-0.410202\pi$
$41$	3.56501	0.556761	0.278380	+	0.960471i	$0.410202\pi$
$42$	5.19141	0.801053
$43$	−7.69760	−1.17387	−0.586936	−	0.809633i	$-0.699666\pi$
$43$	−7.69760	−1.17387	−0.586936	+	0.809633i	$0.699666\pi$
$44$	−0.186969	−0.0281867
$45$	−1.01713	−0.151624
$46$	−1.53315	−0.226050
$47$	5.47953	0.799271	0.399636	−	0.916674i	$-0.369137\pi$
$47$	5.47953	0.799271	0.399636	+	0.916674i	$0.369137\pi$
$48$	1.58539	0.228831
$49$	3.72260	0.531800
$50$	−0.629758	−0.0890612
$51$	4.48454	0.627961
$52$	0	0
$53$	1.39814	0.192049	0.0960247	−	0.995379i	$-0.469387\pi$
$53$	1.39814	0.192049	0.0960247	+	0.995379i	$0.469387\pi$
$54$	−5.52753	−0.752201
$55$	−0.390862	−0.0527038
$56$	3.27454	0.437579
$57$	1.58539	0.209990
$58$	5.03671	0.661352
$59$	−1.94161	−0.252776	−0.126388	−	0.991981i	$-0.540338\pi$
$59$	−1.94161	−0.252776	−0.126388	+	0.991981i	$0.540338\pi$
$60$	3.31427	0.427871
$61$	8.31755	1.06495	0.532477	−	0.846445i	$-0.321261\pi$
$61$	8.31755	1.06495	0.532477	+	0.846445i	$0.321261\pi$
$62$	4.59919	0.584098
$63$	−1.59320	−0.200725
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.296419	−0.0364867
$67$	−1.17201	−0.143183	−0.0715917	−	0.997434i	$-0.522808\pi$
$67$	−1.17201	−0.143183	−0.0715917	+	0.997434i	$0.522808\pi$
$68$	2.82867	0.343027
$69$	−2.43063	−0.292614
$70$	6.84546	0.818189
$71$	3.09652	0.367489	0.183745	−	0.982974i	$-0.441178\pi$
$71$	3.09652	0.367489	0.183745	+	0.982974i	$0.441178\pi$
$72$	−0.486543	−0.0573397
$73$	−11.9094	−1.39388	−0.696942	−	0.717127i	$-0.745457\pi$
$73$	−11.9094	−1.39388	−0.696942	+	0.717127i	$0.745457\pi$
$74$	−2.06596	−0.240163
$75$	−0.998411	−0.115287
$76$	1.00000	0.114708
$77$	−0.612238	−0.0697710
$78$	0	0
$79$	−2.06190	−0.231982	−0.115991	−	0.993250i	$-0.537004\pi$
$79$	−2.06190	−0.231982	−0.115991	+	0.993250i	$0.537004\pi$
$80$	2.09051	0.233726
$81$	−7.30364	−0.811516
$82$	3.56501	0.393689
$83$	13.1907	1.44786	0.723931	−	0.689872i	$-0.242333\pi$
$83$	13.1907	1.44786	0.723931	+	0.689872i	$0.242333\pi$
$84$	5.19141	0.566430
$85$	5.91337	0.641395
$86$	−7.69760	−0.830053
$87$	7.98514	0.856097
$88$	−0.186969	−0.0199310
$89$	−9.20255	−0.975469	−0.487734	−	0.872992i	$-0.662177\pi$
$89$	−9.20255	−0.975469	−0.487734	+	0.872992i	$0.662177\pi$
$90$	−1.01713	−0.107214
$91$	0	0
$92$	−1.53315	−0.159842
$93$	7.29151	0.756094
$94$	5.47953	0.565170
$95$	2.09051	0.214482
$96$	1.58539	0.161808
$97$	−0.735611	−0.0746900	−0.0373450	−	0.999302i	$-0.511890\pi$
$97$	−0.735611	−0.0746900	−0.0373450	+	0.999302i	$0.511890\pi$
$98$	3.72260	0.376039
$99$	0.0909688	0.00914270
$100$	−0.629758	−0.0629758
$101$	0.476982	0.0474615	0.0237307	−	0.999718i	$-0.492446\pi$
$101$	0.476982	0.0474615	0.0237307	+	0.999718i	$0.492446\pi$
$102$	4.48454	0.444036
$103$	14.1205	1.39133	0.695667	−	0.718365i	$-0.255109\pi$
$103$	14.1205	1.39133	0.695667	+	0.718365i	$0.255109\pi$
$104$	0	0
$105$	10.8527	1.05912
$106$	1.39814	0.135800
$107$	3.15753	0.305250	0.152625	−	0.988284i	$-0.451227\pi$
$107$	3.15753	0.305250	0.152625	+	0.988284i	$0.451227\pi$
$108$	−5.52753	−0.531886
$109$	−6.28783	−0.602265	−0.301133	−	0.953582i	$-0.597365\pi$
$109$	−6.28783	−0.602265	−0.301133	+	0.953582i	$0.597365\pi$
$110$	−0.390862	−0.0372672
$111$	−3.27535	−0.310883
$112$	3.27454	0.309415
$113$	10.2831	0.967349	0.483675	−	0.875248i	$-0.339302\pi$
$113$	10.2831	0.967349	0.483675	+	0.875248i	$0.339302\pi$
$114$	1.58539	0.148485
$115$	−3.20506	−0.298874
$116$	5.03671	0.467647
$117$	0	0
$118$	−1.94161	−0.178739
$119$	9.26258	0.849100
$120$	3.31427	0.302550
$121$	−10.9650	−0.996822
$122$	8.31755	0.753036
$123$	5.65192	0.509617
$124$	4.59919	0.413020
$125$	−11.7691	−1.05266
$126$	−1.59320	−0.141934
$127$	−19.9876	−1.77361	−0.886805	−	0.462145i	$-0.847080\pi$
$127$	−19.9876	−1.77361	−0.886805	+	0.462145i	$0.847080\pi$
$128$	1.00000	0.0883883
$129$	−12.2037	−1.07447
$130$	0	0
$131$	−13.8090	−1.20650	−0.603250	−	0.797552i	$-0.706128\pi$
$131$	−13.8090	−1.20650	−0.603250	+	0.797552i	$0.706128\pi$
$132$	−0.296419	−0.0258000
$133$	3.27454	0.283938
$134$	−1.17201	−0.101246
$135$	−11.5554	−0.994527
$136$	2.82867	0.242556
$137$	−7.67043	−0.655329	−0.327664	−	0.944794i	$-0.606262\pi$
$137$	−7.67043	−0.655329	−0.327664	+	0.944794i	$0.606262\pi$
$138$	−2.43063	−0.206909
$139$	10.0736	0.854428	0.427214	−	0.904150i	$-0.359495\pi$
$139$	10.0736	0.854428	0.427214	+	0.904150i	$0.359495\pi$
$140$	6.84546	0.578547
$141$	8.68718	0.731593
$142$	3.09652	0.259854
$143$	0	0
$144$	−0.486543	−0.0405453
$145$	10.5293	0.874411
$146$	−11.9094	−0.985625
$147$	5.90176	0.486769
$148$	−2.06596	−0.169821
$149$	14.3915	1.17900	0.589500	−	0.807769i	$-0.299325\pi$
$149$	14.3915	1.17900	0.589500	+	0.807769i	$0.299325\pi$
$150$	−0.998411	−0.0815199
$151$	7.11851	0.579296	0.289648	−	0.957133i	$-0.406462\pi$
$151$	7.11851	0.579296	0.289648	+	0.957133i	$0.406462\pi$
$152$	1.00000	0.0811107
$153$	−1.37627	−0.111265
$154$	−0.612238	−0.0493356
$155$	9.61467	0.772269
$156$	0	0
$157$	5.77345	0.460772	0.230386	−	0.973099i	$-0.426001\pi$
$157$	5.77345	0.460772	0.230386	+	0.973099i	$0.426001\pi$
$158$	−2.06190	−0.164036
$159$	2.21660	0.175788
$160$	2.09051	0.165270
$161$	−5.02035	−0.395659
$162$	−7.30364	−0.573829
$163$	−12.9136	−1.01147	−0.505735	−	0.862689i	$-0.668779\pi$
$163$	−12.9136	−1.01147	−0.505735	+	0.862689i	$0.668779\pi$
$164$	3.56501	0.278380
$165$	−0.619668	−0.0482411
$166$	13.1907	1.02379
$167$	−18.2725	−1.41397	−0.706985	−	0.707229i	$-0.749945\pi$
$167$	−18.2725	−1.41397	−0.706985	+	0.707229i	$0.749945\pi$
$168$	5.19141	0.400526
$169$	0	0
$170$	5.91337	0.453535
$171$	−0.486543	−0.0372069
$172$	−7.69760	−0.586936
$173$	22.9796	1.74711	0.873554	−	0.486727i	$-0.161809\pi$
$173$	22.9796	1.74711	0.873554	+	0.486727i	$0.161809\pi$
$174$	7.98514	0.605352
$175$	−2.06217	−0.155885
$176$	−0.186969	−0.0140934
$177$	−3.07820	−0.231372
$178$	−9.20255	−0.689761
$179$	−19.0739	−1.42565	−0.712826	−	0.701341i	$-0.752585\pi$
$179$	−19.0739	−1.42565	−0.712826	+	0.701341i	$0.752585\pi$
$180$	−1.01713	−0.0758120
$181$	1.23204	0.0915768	0.0457884	−	0.998951i	$-0.485420\pi$
$181$	1.23204	0.0915768	0.0457884	+	0.998951i	$0.485420\pi$
$182$	0	0
$183$	13.1866	0.974778
$184$	−1.53315	−0.113025
$185$	−4.31892	−0.317533
$186$	7.29151	0.534639
$187$	−0.528875	−0.0386751
$188$	5.47953	0.399636
$189$	−18.1001	−1.31659
$190$	2.09051	0.151662
$191$	25.7248	1.86138	0.930689	−	0.365812i	$-0.119209\pi$
$191$	25.7248	1.86138	0.930689	+	0.365812i	$0.119209\pi$
$192$	1.58539	0.114416
$193$	−4.59176	−0.330522	−0.165261	−	0.986250i	$-0.552847\pi$
$193$	−4.59176	−0.330522	−0.165261	+	0.986250i	$0.552847\pi$
$194$	−0.735611	−0.0528138
$195$	0	0
$196$	3.72260	0.265900
$197$	−20.7226	−1.47643	−0.738213	−	0.674567i	$-0.764330\pi$
$197$	−20.7226	−1.47643	−0.738213	+	0.674567i	$0.764330\pi$
$198$	0.0909688	0.00646487
$199$	22.5815	1.60076	0.800382	−	0.599491i	$-0.204630\pi$
$199$	22.5815	1.60076	0.800382	+	0.599491i	$0.204630\pi$
$200$	−0.629758	−0.0445306
$201$	−1.85808	−0.131059
$202$	0.476982	0.0335603
$203$	16.4929	1.15757
$204$	4.48454	0.313981
$205$	7.45269	0.520519
$206$	14.1205	0.983822
$207$	0.745943	0.0518466
$208$	0	0
$209$	−0.186969	−0.0129329
$210$	10.8527	0.748909
$211$	−18.5783	−1.27899	−0.639493	−	0.768797i	$-0.720856\pi$
$211$	−18.5783	−1.27899	−0.639493	+	0.768797i	$0.720856\pi$
$212$	1.39814	0.0960247
$213$	4.90919	0.336372
$214$	3.15753	0.215844
$215$	−16.0919	−1.09746
$216$	−5.52753	−0.376100
$217$	15.0602	1.02235
$218$	−6.28783	−0.425866
$219$	−18.8810	−1.27586
$220$	−0.390862	−0.0263519
$221$	0	0
$222$	−3.27535	−0.219827
$223$	−3.16144	−0.211706	−0.105853	−	0.994382i	$-0.533757\pi$
$223$	−3.16144	−0.211706	−0.105853	+	0.994382i	$0.533757\pi$
$224$	3.27454	0.218789
$225$	0.306405	0.0204270
$226$	10.2831	0.684019
$227$	−5.01391	−0.332785	−0.166393	−	0.986060i	$-0.553212\pi$
$227$	−5.01391	−0.332785	−0.166393	+	0.986060i	$0.553212\pi$
$228$	1.58539	0.104995
$229$	−19.2863	−1.27448	−0.637238	−	0.770667i	$-0.719923\pi$
$229$	−19.2863	−1.27448	−0.637238	+	0.770667i	$0.719923\pi$
$230$	−3.20506	−0.211336
$231$	−0.970636	−0.0638631
$232$	5.03671	0.330676
$233$	−14.3970	−0.943180	−0.471590	−	0.881818i	$-0.656320\pi$
$233$	−14.3970	−0.943180	−0.471590	+	0.881818i	$0.656320\pi$
$234$	0	0
$235$	11.4550	0.747243
$236$	−1.94161	−0.126388
$237$	−3.26891	−0.212339
$238$	9.26258	0.600404
$239$	−1.88105	−0.121675	−0.0608374	−	0.998148i	$-0.519377\pi$
$239$	−1.88105	−0.121675	−0.0608374	+	0.998148i	$0.519377\pi$
$240$	3.31427	0.213935
$241$	−5.22432	−0.336528	−0.168264	−	0.985742i	$-0.553816\pi$
$241$	−5.22432	−0.336528	−0.168264	+	0.985742i	$0.553816\pi$
$242$	−10.9650	−0.704860
$243$	5.00346	0.320972
$244$	8.31755	0.532477
$245$	7.78213	0.497182
$246$	5.65192	0.360353
$247$	0	0
$248$	4.59919	0.292049
$249$	20.9123	1.32526
$250$	−11.7691	−0.744342
$251$	−9.28189	−0.585868	−0.292934	−	0.956133i	$-0.594632\pi$
$251$	−9.28189	−0.585868	−0.292934	+	0.956133i	$0.594632\pi$
$252$	−1.59320	−0.100362
$253$	0.286652	0.0180216
$254$	−19.9876	−1.25413
$255$	9.37499	0.587084
$256$	1.00000	0.0625000
$257$	−21.9917	−1.37181	−0.685903	−	0.727693i	$-0.740593\pi$
$257$	−21.9917	−1.37181	−0.685903	+	0.727693i	$0.740593\pi$
$258$	−12.2037	−0.759768
$259$	−6.76507	−0.420361
$260$	0	0
$261$	−2.45058	−0.151687
$262$	−13.8090	−0.853124
$263$	8.03621	0.495534	0.247767	−	0.968820i	$-0.420303\pi$
$263$	8.03621	0.495534	0.247767	+	0.968820i	$0.420303\pi$
$264$	−0.296419	−0.0182433
$265$	2.92283	0.179548
$266$	3.27454	0.200775
$267$	−14.5896	−0.892870
$268$	−1.17201	−0.0715917
$269$	24.8004	1.51211	0.756054	−	0.654509i	$-0.227125\pi$
$269$	24.8004	1.51211	0.756054	+	0.654509i	$0.227125\pi$
$270$	−11.5554	−0.703237
$271$	−21.5700	−1.31029	−0.655143	−	0.755505i	$-0.727392\pi$
$271$	−21.5700	−1.31029	−0.655143	+	0.755505i	$0.727392\pi$
$272$	2.82867	0.171513
$273$	0	0
$274$	−7.67043	−0.463387
$275$	0.117745	0.00710032
$276$	−2.43063	−0.146307
$277$	25.5359	1.53430	0.767152	−	0.641466i	$-0.221673\pi$
$277$	25.5359	1.53430	0.767152	+	0.641466i	$0.221673\pi$
$278$	10.0736	0.604172
$279$	−2.23771	−0.133968
$280$	6.84546	0.409095
$281$	−5.44427	−0.324778	−0.162389	−	0.986727i	$-0.551920\pi$
$281$	−5.44427	−0.324778	−0.162389	+	0.986727i	$0.551920\pi$
$282$	8.68718	0.517314
$283$	15.3503	0.912481	0.456240	−	0.889857i	$-0.349196\pi$
$283$	15.3503	0.912481	0.456240	+	0.889857i	$0.349196\pi$
$284$	3.09652	0.183745
$285$	3.31427	0.196321
$286$	0	0
$287$	11.6738	0.689080
$288$	−0.486543	−0.0286698
$289$	−8.99863	−0.529331
$290$	10.5293	0.618302
$291$	−1.16623	−0.0683656
$292$	−11.9094	−0.696942
$293$	−14.6429	−0.855449	−0.427725	−	0.903909i	$-0.640685\pi$
$293$	−14.6429	−0.855449	−0.427725	+	0.903909i	$0.640685\pi$
$294$	5.90176	0.344198
$295$	−4.05895	−0.236321
$296$	−2.06596	−0.120082
$297$	1.03348	0.0599685
$298$	14.3915	0.833678
$299$	0	0
$300$	−0.998411	−0.0576433
$301$	−25.2061	−1.45285
$302$	7.11851	0.409624
$303$	0.756202	0.0434427
$304$	1.00000	0.0573539
$305$	17.3879	0.995631
$306$	−1.37627	−0.0786762
$307$	12.0967	0.690393	0.345197	−	0.938530i	$-0.387812\pi$
$307$	12.0967	0.690393	0.345197	+	0.938530i	$0.387812\pi$
$308$	−0.612238	−0.0348855
$309$	22.3865	1.27352
$310$	9.61467	0.546076
$311$	−18.4710	−1.04739	−0.523696	−	0.851905i	$-0.675447\pi$
$311$	−18.4710	−1.04739	−0.523696	+	0.851905i	$0.675447\pi$
$312$	0	0
$313$	30.4654	1.72201	0.861004	−	0.508599i	$-0.169836\pi$
$313$	30.4654	1.72201	0.861004	+	0.508599i	$0.169836\pi$
$314$	5.77345	0.325815
$315$	−3.33061	−0.187659
$316$	−2.06190	−0.115991
$317$	−13.6573	−0.767072	−0.383536	−	0.923526i	$-0.625294\pi$
$317$	−13.6573	−0.767072	−0.383536	+	0.923526i	$0.625294\pi$
$318$	2.21660	0.124301
$319$	−0.941711	−0.0527257
$320$	2.09051	0.116863
$321$	5.00591	0.279403
$322$	−5.02035	−0.279773
$323$	2.82867	0.157391
$324$	−7.30364	−0.405758
$325$	0	0
$326$	−12.9136	−0.715218
$327$	−9.96866	−0.551268
$328$	3.56501	0.196845
$329$	17.9429	0.989225
$330$	−0.619668	−0.0341116
$331$	−16.3053	−0.896219	−0.448110	−	0.893979i	$-0.647903\pi$
$331$	−16.3053	−0.896219	−0.448110	+	0.893979i	$0.647903\pi$
$332$	13.1907	0.723931
$333$	1.00518	0.0550836
$334$	−18.2725	−0.999827
$335$	−2.45009	−0.133863
$336$	5.19141	0.283215
$337$	20.4360	1.11322	0.556611	−	0.830773i	$-0.312102\pi$
$337$	20.4360	1.11322	0.556611	+	0.830773i	$0.312102\pi$
$338$	0	0
$339$	16.3026	0.885438
$340$	5.91337	0.320697
$341$	−0.859908	−0.0465666
$342$	−0.486543	−0.0263093
$343$	−10.7320	−0.579472
$344$	−7.69760	−0.415027
$345$	−5.08127	−0.273566
$346$	22.9796	1.23539
$347$	−18.8747	−1.01325	−0.506624	−	0.862167i	$-0.669107\pi$
$347$	−18.8747	−1.01325	−0.506624	+	0.862167i	$0.669107\pi$
$348$	7.98514	0.428049
$349$	1.01303	0.0542260	0.0271130	−	0.999632i	$-0.491369\pi$
$349$	1.01303	0.0542260	0.0271130	+	0.999632i	$0.491369\pi$
$350$	−2.06217	−0.110227
$351$	0	0
$352$	−0.186969	−0.00996550
$353$	26.8906	1.43124	0.715620	−	0.698489i	$-0.246144\pi$
$353$	26.8906	1.43124	0.715620	+	0.698489i	$0.246144\pi$
$354$	−3.07820	−0.163605
$355$	6.47331	0.343568
$356$	−9.20255	−0.487734
$357$	14.6848	0.777202
$358$	−19.0739	−1.00809
$359$	−2.38222	−0.125729	−0.0628644	−	0.998022i	$-0.520024\pi$
$359$	−2.38222	−0.125729	−0.0628644	+	0.998022i	$0.520024\pi$
$360$	−1.01713	−0.0536072
$361$	1.00000	0.0526316
$362$	1.23204	0.0647546
$363$	−17.3839	−0.912416
$364$	0	0
$365$	−24.8967	−1.30315
$366$	13.1866	0.689272
$367$	−10.3958	−0.542657	−0.271329	−	0.962487i	$-0.587463\pi$
$367$	−10.3958	−0.542657	−0.271329	+	0.962487i	$0.587463\pi$
$368$	−1.53315	−0.0799208
$369$	−1.73453	−0.0902961
$370$	−4.31892	−0.224530
$371$	4.57827	0.237692
$372$	7.29151	0.378047
$373$	−15.0363	−0.778550	−0.389275	−	0.921122i	$-0.627274\pi$
$373$	−15.0363	−0.778550	−0.389275	+	0.921122i	$0.627274\pi$
$374$	−0.528875	−0.0273475
$375$	−18.6586	−0.963524
$376$	5.47953	0.282585
$377$	0	0
$378$	−18.1001	−0.930968
$379$	−36.2666	−1.86289	−0.931445	−	0.363883i	$-0.881451\pi$
$379$	−36.2666	−1.86289	−0.931445	+	0.363883i	$0.881451\pi$
$380$	2.09051	0.107241
$381$	−31.6880	−1.62343
$382$	25.7248	1.31619
$383$	−10.1971	−0.521049	−0.260525	−	0.965467i	$-0.583896\pi$
$383$	−10.1971	−0.521049	−0.260525	+	0.965467i	$0.583896\pi$
$384$	1.58539	0.0809040
$385$	−1.27989	−0.0652293
$386$	−4.59176	−0.233714
$387$	3.74521	0.190380
$388$	−0.735611	−0.0373450
$389$	−35.0114	−1.77515	−0.887575	−	0.460663i	$-0.847612\pi$
$389$	−35.0114	−1.77515	−0.887575	+	0.460663i	$0.847612\pi$
$390$	0	0
$391$	−4.33677	−0.219320
$392$	3.72260	0.188020
$393$	−21.8927	−1.10434
$394$	−20.7226	−1.04399
$395$	−4.31043	−0.216881
$396$	0.0909688	0.00457135
$397$	15.2888	0.767324	0.383662	−	0.923474i	$-0.374663\pi$
$397$	15.2888	0.767324	0.383662	+	0.923474i	$0.374663\pi$
$398$	22.5815	1.13191
$399$	5.19141	0.259896
$400$	−0.629758	−0.0314879
$401$	7.01299	0.350212	0.175106	−	0.984550i	$-0.443973\pi$
$401$	7.01299	0.350212	0.175106	+	0.984550i	$0.443973\pi$
$402$	−1.85808	−0.0926728
$403$	0	0
$404$	0.476982	0.0237307
$405$	−15.2684	−0.758691
$406$	16.4929	0.818529
$407$	0.386272	0.0191468
$408$	4.48454	0.222018
$409$	−13.9843	−0.691477	−0.345739	−	0.938331i	$-0.612372\pi$
$409$	−13.9843	−0.691477	−0.345739	+	0.938331i	$0.612372\pi$
$410$	7.45269	0.368062
$411$	−12.1606	−0.599838
$412$	14.1205	0.695667
$413$	−6.35787	−0.312850
$414$	0.745943	0.0366611
$415$	27.5752	1.35362
$416$	0	0
$417$	15.9705	0.782079
$418$	−0.186969	−0.00914497
$419$	−37.5807	−1.83594	−0.917968	−	0.396655i	$-0.870171\pi$
$419$	−37.5807	−1.83594	−0.917968	+	0.396655i	$0.870171\pi$
$420$	10.8527	0.529558
$421$	30.9744	1.50960	0.754801	−	0.655954i	$-0.227734\pi$
$421$	30.9744	1.50960	0.754801	+	0.655954i	$0.227734\pi$
$422$	−18.5783	−0.904379
$423$	−2.66603	−0.129627
$424$	1.39814	0.0678998
$425$	−1.78138	−0.0864095
$426$	4.90919	0.237851
$427$	27.2361	1.31805
$428$	3.15753	0.152625
$429$	0	0
$430$	−16.0919	−0.776021
$431$	−24.3514	−1.17296	−0.586482	−	0.809962i	$-0.699488\pi$
$431$	−24.3514	−1.17296	−0.586482	+	0.809962i	$0.699488\pi$
$432$	−5.52753	−0.265943
$433$	14.6349	0.703310	0.351655	−	0.936130i	$-0.385619\pi$
$433$	14.6349	0.703310	0.351655	+	0.936130i	$0.385619\pi$
$434$	15.0602	0.722914
$435$	16.6930	0.800370
$436$	−6.28783	−0.301133
$437$	−1.53315	−0.0733404
$438$	−18.8810	−0.902167
$439$	31.3719	1.49730	0.748650	−	0.662965i	$-0.230702\pi$
$439$	31.3719	1.49730	0.748650	+	0.662965i	$0.230702\pi$
$440$	−0.390862	−0.0186336
$441$	−1.81121	−0.0862479
$442$	0	0
$443$	−24.4634	−1.16229	−0.581145	−	0.813800i	$-0.697395\pi$
$443$	−24.4634	−1.16229	−0.581145	+	0.813800i	$0.697395\pi$
$444$	−3.27535	−0.155441
$445$	−19.2381	−0.911971
$446$	−3.16144	−0.149698
$447$	22.8161	1.07917
$448$	3.27454	0.154707
$449$	−32.5272	−1.53505	−0.767527	−	0.641017i	$-0.778513\pi$
$449$	−32.5272	−1.53505	−0.767527	+	0.641017i	$0.778513\pi$
$450$	0.306405	0.0144441
$451$	−0.666548	−0.0313865
$452$	10.2831	0.483675
$453$	11.2856	0.530244
$454$	−5.01391	−0.235315
$455$	0	0
$456$	1.58539	0.0742426
$457$	−15.7954	−0.738876	−0.369438	−	0.929255i	$-0.620450\pi$
$457$	−15.7954	−0.738876	−0.369438	+	0.929255i	$0.620450\pi$
$458$	−19.2863	−0.901191
$459$	−15.6355	−0.729805
$460$	−3.20506	−0.149437
$461$	30.7808	1.43361	0.716803	−	0.697276i	$-0.245605\pi$
$461$	30.7808	1.43361	0.716803	+	0.697276i	$0.245605\pi$
$462$	−0.970636	−0.0451581
$463$	35.3937	1.64488	0.822442	−	0.568848i	$-0.192611\pi$
$463$	35.3937	1.64488	0.822442	+	0.568848i	$0.192611\pi$
$464$	5.03671	0.233823
$465$	15.2430	0.706876
$466$	−14.3970	−0.666929
$467$	−2.38161	−0.110208	−0.0551039	−	0.998481i	$-0.517549\pi$
$467$	−2.38161	−0.110208	−0.0551039	+	0.998481i	$0.517549\pi$
$468$	0	0
$469$	−3.83778	−0.177212
$470$	11.4550	0.528381
$471$	9.15317	0.421756
$472$	−1.94161	−0.0893697
$473$	1.43922	0.0661752
$474$	−3.26891	−0.150146
$475$	−0.629758	−0.0288953
$476$	9.26258	0.424550
$477$	−0.680257	−0.0311468
$478$	−1.88105	−0.0860371
$479$	26.1204	1.19347	0.596737	−	0.802437i	$-0.296464\pi$
$479$	26.1204	1.19347	0.596737	+	0.802437i	$0.296464\pi$
$480$	3.31427	0.151275
$481$	0	0
$482$	−5.22432	−0.237961
$483$	−7.95920	−0.362156
$484$	−10.9650	−0.498411
$485$	−1.53780	−0.0698281
$486$	5.00346	0.226962
$487$	−7.08808	−0.321191	−0.160596	−	0.987020i	$-0.551342\pi$
$487$	−7.08808	−0.321191	−0.160596	+	0.987020i	$0.551342\pi$
$488$	8.31755	0.376518
$489$	−20.4731	−0.925824
$490$	7.78213	0.351561
$491$	−1.18086	−0.0532916	−0.0266458	−	0.999645i	$-0.508483\pi$
$491$	−1.18086	−0.0532916	−0.0266458	+	0.999645i	$0.508483\pi$
$492$	5.65192	0.254808
$493$	14.2472	0.641661
$494$	0	0
$495$	0.190171	0.00854757
$496$	4.59919	0.206510
$497$	10.1397	0.454826
$498$	20.9123	0.937103
$499$	−1.61241	−0.0721814	−0.0360907	−	0.999349i	$-0.511491\pi$
$499$	−1.61241	−0.0721814	−0.0360907	+	0.999349i	$0.511491\pi$
$500$	−11.7691	−0.526329
$501$	−28.9690	−1.29424
$502$	−9.28189	−0.414271
$503$	2.38399	0.106297	0.0531485	−	0.998587i	$-0.483074\pi$
$503$	2.38399	0.106297	0.0531485	+	0.998587i	$0.483074\pi$
$504$	−1.59320	−0.0709670
$505$	0.997137	0.0443720
$506$	0.286652	0.0127432
$507$	0	0
$508$	−19.9876	−0.886805
$509$	37.4929	1.66184	0.830921	−	0.556391i	$-0.187814\pi$
$509$	37.4929	1.66184	0.830921	+	0.556391i	$0.187814\pi$
$510$	9.37499	0.415131
$511$	−38.9976	−1.72515
$512$	1.00000	0.0441942
$513$	−5.52753	−0.244046
$514$	−21.9917	−0.970013
$515$	29.5191	1.30077
$516$	−12.2037	−0.537237
$517$	−1.02450	−0.0450577
$518$	−6.76507	−0.297240
$519$	36.4316	1.59917
$520$	0	0
$521$	19.6147	0.859337	0.429668	−	0.902987i	$-0.358630\pi$
$521$	19.6147	0.859337	0.429668	+	0.902987i	$0.358630\pi$
$522$	−2.45058	−0.107259
$523$	41.2190	1.80238	0.901190	−	0.433424i	$-0.142695\pi$
$523$	41.2190	1.80238	0.901190	+	0.433424i	$0.142695\pi$
$524$	−13.8090	−0.603250
$525$	−3.26933	−0.142685
$526$	8.03621	0.350395
$527$	13.0096	0.566707
$528$	−0.296419	−0.0129000
$529$	−20.6495	−0.897803
$530$	2.92283	0.126960
$531$	0.944676	0.0409955
$532$	3.27454	0.141969
$533$	0	0
$534$	−14.5896	−0.631355
$535$	6.60085	0.285380
$536$	−1.17201	−0.0506229
$537$	−30.2396	−1.30493
$538$	24.8004	1.06922
$539$	−0.696012	−0.0299794
$540$	−11.5554	−0.497264
$541$	−12.1333	−0.521653	−0.260827	−	0.965386i	$-0.583995\pi$
$541$	−12.1333	−0.521653	−0.260827	+	0.965386i	$0.583995\pi$
$542$	−21.5700	−0.926512
$543$	1.95326	0.0838225
$544$	2.82867	0.121278
$545$	−13.1448	−0.563061
$546$	0	0
$547$	18.6601	0.797849	0.398924	−	0.916984i	$-0.369384\pi$
$547$	18.6601	0.797849	0.398924	+	0.916984i	$0.369384\pi$
$548$	−7.67043	−0.327664
$549$	−4.04685	−0.172715
$550$	0.117745	0.00502068
$551$	5.03671	0.214571
$552$	−2.43063	−0.103455
$553$	−6.75177	−0.287114
$554$	25.5359	1.08492
$555$	−6.84717	−0.290646
$556$	10.0736	0.427214
$557$	17.1833	0.728080	0.364040	−	0.931383i	$-0.381397\pi$
$557$	17.1833	0.728080	0.364040	+	0.931383i	$0.381397\pi$
$558$	−2.23771	−0.0947297
$559$	0	0
$560$	6.84546	0.289274
$561$	−0.838472	−0.0354003
$562$	−5.44427	−0.229653
$563$	−27.5192	−1.15980	−0.579898	−	0.814689i	$-0.696908\pi$
$563$	−27.5192	−1.15980	−0.579898	+	0.814689i	$0.696908\pi$
$564$	8.68718	0.365796
$565$	21.4969	0.904380
$566$	15.3503	0.645221
$567$	−23.9161	−1.00438
$568$	3.09652	0.129927
$569$	17.7673	0.744845	0.372423	−	0.928063i	$-0.378527\pi$
$569$	17.7673	0.744845	0.372423	+	0.928063i	$0.378527\pi$
$570$	3.31427	0.138820
$571$	14.3951	0.602417	0.301208	−	0.953558i	$-0.402610\pi$
$571$	14.3951	0.602417	0.301208	+	0.953558i	$0.402610\pi$
$572$	0	0
$573$	40.7837	1.70376
$574$	11.6738	0.487253
$575$	0.965512	0.0402646
$576$	−0.486543	−0.0202726
$577$	−11.9841	−0.498905	−0.249452	−	0.968387i	$-0.580251\pi$
$577$	−11.9841	−0.498905	−0.249452	+	0.968387i	$0.580251\pi$
$578$	−8.99863	−0.374294
$579$	−7.27972	−0.302535
$580$	10.5293	0.437206
$581$	43.1933	1.79196
$582$	−1.16623	−0.0483418
$583$	−0.261410	−0.0108265
$584$	−11.9094	−0.492813
$585$	0	0
$586$	−14.6429	−0.604894
$587$	5.27354	0.217662	0.108831	−	0.994060i	$-0.465289\pi$
$587$	5.27354	0.217662	0.108831	+	0.994060i	$0.465289\pi$
$588$	5.90176	0.243385
$589$	4.59919	0.189506
$590$	−4.05895	−0.167104
$591$	−32.8534	−1.35141
$592$	−2.06596	−0.0849106
$593$	32.6576	1.34109	0.670543	−	0.741871i	$-0.266061\pi$
$593$	32.6576	1.34109	0.670543	+	0.741871i	$0.266061\pi$
$594$	1.03348	0.0424041
$595$	19.3635	0.793828
$596$	14.3915	0.589500
$597$	35.8005	1.46522
$598$	0	0
$599$	36.3390	1.48477	0.742387	−	0.669972i	$-0.233694\pi$
$599$	36.3390	1.48477	0.742387	+	0.669972i	$0.233694\pi$
$600$	−0.998411	−0.0407600
$601$	−25.4042	−1.03626	−0.518129	−	0.855302i	$-0.673371\pi$
$601$	−25.4042	−1.03626	−0.518129	+	0.855302i	$0.673371\pi$
$602$	−25.2061	−1.02732
$603$	0.570232	0.0232216
$604$	7.11851	0.289648
$605$	−22.9226	−0.931934
$606$	0.756202	0.0307186
$607$	34.1626	1.38662	0.693308	−	0.720641i	$-0.256152\pi$
$607$	34.1626	1.38662	0.693308	+	0.720641i	$0.256152\pi$
$608$	1.00000	0.0405554
$609$	26.1476	1.05956
$610$	17.3879	0.704017
$611$	0	0
$612$	−1.37627	−0.0556324
$613$	19.7897	0.799299	0.399650	−	0.916668i	$-0.369132\pi$
$613$	19.7897	0.799299	0.399650	+	0.916668i	$0.369132\pi$
$614$	12.0967	0.488182
$615$	11.8154	0.476443
$616$	−0.612238	−0.0246678
$617$	−24.8150	−0.999014	−0.499507	−	0.866310i	$-0.666486\pi$
$617$	−24.8150	−0.999014	−0.499507	+	0.866310i	$0.666486\pi$
$618$	22.3865	0.900516
$619$	17.2395	0.692912	0.346456	−	0.938066i	$-0.387385\pi$
$619$	17.2395	0.692912	0.346456	+	0.938066i	$0.387385\pi$
$620$	9.61467	0.386134
$621$	8.47451	0.340070
$622$	−18.4710	−0.740618
$623$	−30.1341	−1.20730
$624$	0	0
$625$	−21.4546	−0.858185
$626$	30.4654	1.21764
$627$	−0.296419	−0.0118378
$628$	5.77345	0.230386
$629$	−5.84393	−0.233013
$630$	−3.33061	−0.132695
$631$	25.1780	1.00232	0.501160	−	0.865355i	$-0.332907\pi$
$631$	25.1780	1.00232	0.501160	+	0.865355i	$0.332907\pi$
$632$	−2.06190	−0.0820180
$633$	−29.4539	−1.17069
$634$	−13.6573	−0.542402
$635$	−41.7842	−1.65816
$636$	2.21660	0.0878938
$637$	0	0
$638$	−0.941711	−0.0372827
$639$	−1.50659	−0.0595998
$640$	2.09051	0.0826348
$641$	−3.97802	−0.157122	−0.0785611	−	0.996909i	$-0.525033\pi$
$641$	−3.97802	−0.157122	−0.0785611	+	0.996909i	$0.525033\pi$
$642$	5.00591	0.197567
$643$	−10.4851	−0.413491	−0.206746	−	0.978395i	$-0.566287\pi$
$643$	−10.4851	−0.413491	−0.206746	+	0.978395i	$0.566287\pi$
$644$	−5.02035	−0.197829
$645$	−25.5119	−1.00453
$646$	2.82867	0.111293
$647$	−16.2506	−0.638876	−0.319438	−	0.947607i	$-0.603494\pi$
$647$	−16.2506	−0.638876	−0.319438	+	0.947607i	$0.603494\pi$
$648$	−7.30364	−0.286914
$649$	0.363021	0.0142498
$650$	0	0
$651$	23.8763	0.935786
$652$	−12.9136	−0.505735
$653$	4.72836	0.185035	0.0925176	−	0.995711i	$-0.470509\pi$
$653$	4.72836	0.185035	0.0925176	+	0.995711i	$0.470509\pi$
$654$	−9.96866	−0.389805
$655$	−28.8679	−1.12796
$656$	3.56501	0.139190
$657$	5.79442	0.226062
$658$	17.9429	0.699488
$659$	16.9070	0.658602	0.329301	−	0.944225i	$-0.393187\pi$
$659$	16.9070	0.658602	0.329301	+	0.944225i	$0.393187\pi$
$660$	−0.619668	−0.0241205
$661$	−46.0438	−1.79090	−0.895448	−	0.445165i	$-0.853145\pi$
$661$	−46.0438	−1.79090	−0.895448	+	0.445165i	$0.853145\pi$
$662$	−16.3053	−0.633723
$663$	0	0
$664$	13.1907	0.511897
$665$	6.84546	0.265456
$666$	1.00518	0.0389500
$667$	−7.72202	−0.298998
$668$	−18.2725	−0.706985
$669$	−5.01211	−0.193779
$670$	−2.45009	−0.0946554
$671$	−1.55513	−0.0600351
$672$	5.19141	0.200263
$673$	−31.1396	−1.20034	−0.600172	−	0.799871i	$-0.704901\pi$
$673$	−31.1396	−1.20034	−0.600172	+	0.799871i	$0.704901\pi$
$674$	20.4360	0.787166
$675$	3.48100	0.133984
$676$	0	0
$677$	−35.6293	−1.36935	−0.684673	−	0.728850i	$-0.740055\pi$
$677$	−35.6293	−1.36935	−0.684673	+	0.728850i	$0.740055\pi$
$678$	16.3026	0.626099
$679$	−2.40879	−0.0924407
$680$	5.91337	0.226767
$681$	−7.94900	−0.304606
$682$	−0.859908	−0.0329276
$683$	1.63801	0.0626767	0.0313384	−	0.999509i	$-0.490023\pi$
$683$	1.63801	0.0626767	0.0313384	+	0.999509i	$0.490023\pi$
$684$	−0.486543	−0.0186035
$685$	−16.0351	−0.612671
$686$	−10.7320	−0.409749
$687$	−30.5763	−1.16656
$688$	−7.69760	−0.293468
$689$	0	0
$690$	−5.08127	−0.193441
$691$	4.35017	0.165488	0.0827441	−	0.996571i	$-0.473632\pi$
$691$	4.35017	0.165488	0.0827441	+	0.996571i	$0.473632\pi$
$692$	22.9796	0.873554
$693$	0.297881	0.0113155
$694$	−18.8747	−0.716475
$695$	21.0589	0.798810
$696$	7.98514	0.302676
$697$	10.0842	0.381967
$698$	1.01303	0.0383436
$699$	−22.8249	−0.863316
$700$	−2.06217	−0.0779425
$701$	−6.20500	−0.234360	−0.117180	−	0.993111i	$-0.537385\pi$
$701$	−6.20500	−0.234360	−0.117180	+	0.993111i	$0.537385\pi$
$702$	0	0
$703$	−2.06596	−0.0779193
$704$	−0.186969	−0.00704668
$705$	18.1607	0.683970
$706$	26.8906	1.01204
$707$	1.56190	0.0587411
$708$	−3.07820	−0.115686
$709$	11.3224	0.425223	0.212611	−	0.977137i	$-0.431803\pi$
$709$	11.3224	0.425223	0.212611	+	0.977137i	$0.431803\pi$
$710$	6.47331	0.242939
$711$	1.00320	0.0376231
$712$	−9.20255	−0.344880
$713$	−7.05124	−0.264071
$714$	14.6848	0.549565
$715$	0	0
$716$	−19.0739	−0.712826
$717$	−2.98219	−0.111372
$718$	−2.38222	−0.0889036
$719$	8.99694	0.335529	0.167765	−	0.985827i	$-0.446345\pi$
$719$	8.99694	0.335529	0.167765	+	0.985827i	$0.446345\pi$
$720$	−1.01713	−0.0379060
$721$	46.2381	1.72200
$722$	1.00000	0.0372161
$723$	−8.28258	−0.308032
$724$	1.23204	0.0457884
$725$	−3.17191	−0.117802
$726$	−17.3839	−0.645175
$727$	−2.52570	−0.0936730	−0.0468365	−	0.998903i	$-0.514914\pi$
$727$	−2.52570	−0.0936730	−0.0468365	+	0.998903i	$0.514914\pi$
$728$	0	0
$729$	29.8434	1.10531
$730$	−24.8967	−0.921466
$731$	−21.7740	−0.805339
$732$	13.1866	0.487389
$733$	6.30432	0.232856	0.116428	−	0.993199i	$-0.462856\pi$
$733$	6.30432	0.232856	0.116428	+	0.993199i	$0.462856\pi$
$734$	−10.3958	−0.383717
$735$	12.3377	0.455083
$736$	−1.53315	−0.0565126
$737$	0.219129	0.00807173
$738$	−1.73453	−0.0638490
$739$	−28.6982	−1.05568	−0.527841	−	0.849343i	$-0.676998\pi$
$739$	−28.6982	−1.05568	−0.527841	+	0.849343i	$0.676998\pi$
$740$	−4.31892	−0.158767
$741$	0	0
$742$	4.57827	0.168073
$743$	29.2903	1.07456	0.537279	−	0.843405i	$-0.319452\pi$
$743$	29.2903	1.07456	0.537279	+	0.843405i	$0.319452\pi$
$744$	7.29151	0.267320
$745$	30.0856	1.10225
$746$	−15.0363	−0.550518
$747$	−6.41783	−0.234816
$748$	−0.528875	−0.0193376
$749$	10.3394	0.377795
$750$	−18.6586	−0.681314
$751$	−2.75204	−0.100423	−0.0502117	−	0.998739i	$-0.515990\pi$
$751$	−2.75204	−0.100423	−0.0502117	+	0.998739i	$0.515990\pi$
$752$	5.47953	0.199818
$753$	−14.7154	−0.536259
$754$	0	0
$755$	14.8813	0.541587
$756$	−18.1001	−0.658294
$757$	46.7466	1.69903	0.849517	−	0.527562i	$-0.176894\pi$
$757$	46.7466	1.69903	0.849517	+	0.527562i	$0.176894\pi$
$758$	−36.2666	−1.31726
$759$	0.454454	0.0164956
$760$	2.09051	0.0758309
$761$	−29.1446	−1.05649	−0.528245	−	0.849092i	$-0.677150\pi$
$761$	−29.1446	−1.05649	−0.528245	+	0.849092i	$0.677150\pi$
$762$	−31.6880	−1.14794
$763$	−20.5897	−0.745399
$764$	25.7248	0.930689
$765$	−2.87711	−0.104022
$766$	−10.1971	−0.368438
$767$	0	0
$768$	1.58539	0.0572078
$769$	42.2162	1.52235	0.761177	−	0.648544i	$-0.224622\pi$
$769$	42.2162	1.52235	0.761177	+	0.648544i	$0.224622\pi$
$770$	−1.27989	−0.0461241
$771$	−34.8654	−1.25565
$772$	−4.59176	−0.165261
$773$	−19.7189	−0.709241	−0.354620	−	0.935010i	$-0.615390\pi$
$773$	−19.7189	−0.709241	−0.354620	+	0.935010i	$0.615390\pi$
$774$	3.74521	0.134619
$775$	−2.89638	−0.104041
$776$	−0.735611	−0.0264069
$777$	−10.7253	−0.384767
$778$	−35.0114	−1.25522
$779$	3.56501	0.127730
$780$	0	0
$781$	−0.578954	−0.0207166
$782$	−4.33677	−0.155082
$783$	−27.8405	−0.994940
$784$	3.72260	0.132950
$785$	12.0695	0.430778
$786$	−21.8927	−0.780885
$787$	39.3809	1.40378	0.701888	−	0.712287i	$-0.252341\pi$
$787$	39.3809	1.40378	0.701888	+	0.712287i	$0.252341\pi$
$788$	−20.7226	−0.738213
$789$	12.7405	0.453574
$790$	−4.31043	−0.153358
$791$	33.6723	1.19725
$792$	0.0909688	0.00323243
$793$	0	0
$794$	15.2888	0.542580
$795$	4.63382	0.164345
$796$	22.5815	0.800382
$797$	15.2535	0.540305	0.270153	−	0.962818i	$-0.412926\pi$
$797$	15.2535	0.540305	0.270153	+	0.962818i	$0.412926\pi$
$798$	5.19141	0.183774
$799$	15.4998	0.548343
$800$	−0.629758	−0.0222653
$801$	4.47744	0.158203
$802$	7.01299	0.247637
$803$	2.22669	0.0785780
$804$	−1.85808	−0.0655296
$805$	−10.4951	−0.369904
$806$	0	0
$807$	39.3183	1.38407
$808$	0.476982	0.0167802
$809$	−38.5105	−1.35396	−0.676978	−	0.736003i	$-0.736711\pi$
$809$	−38.5105	−1.35396	−0.676978	+	0.736003i	$0.736711\pi$
$810$	−15.2684	−0.536476
$811$	−23.0976	−0.811067	−0.405534	−	0.914080i	$-0.632914\pi$
$811$	−23.0976	−0.811067	−0.405534	+	0.914080i	$0.632914\pi$
$812$	16.4929	0.578787
$813$	−34.1969	−1.19934
$814$	0.386272	0.0135388
$815$	−26.9960	−0.945630
$816$	4.48454	0.156990
$817$	−7.69760	−0.269305
$818$	−13.9843	−0.488948
$819$	0	0
$820$	7.45269	0.260259
$821$	−48.4638	−1.69140	−0.845700	−	0.533659i	$-0.820817\pi$
$821$	−48.4638	−1.69140	−0.845700	+	0.533659i	$0.820817\pi$
$822$	−12.1606	−0.424150
$823$	20.8824	0.727914	0.363957	−	0.931416i	$-0.381426\pi$
$823$	20.8824	0.727914	0.363957	+	0.931416i	$0.381426\pi$
$824$	14.1205	0.491911
$825$	0.186672	0.00649910
$826$	−6.35787	−0.221218
$827$	11.7921	0.410050	0.205025	−	0.978757i	$-0.434272\pi$
$827$	11.7921	0.410050	0.205025	+	0.978757i	$0.434272\pi$
$828$	0.745943	0.0259233
$829$	−5.42983	−0.188586	−0.0942928	−	0.995545i	$-0.530059\pi$
$829$	−5.42983	−0.188586	−0.0942928	+	0.995545i	$0.530059\pi$
$830$	27.5752	0.957150
$831$	40.4843	1.40439
$832$	0	0
$833$	10.5300	0.364843
$834$	15.9705	0.553013
$835$	−38.1989	−1.32193
$836$	−0.186969	−0.00646647
$837$	−25.4222	−0.878718
$838$	−37.5807	−1.29820
$839$	−18.4660	−0.637517	−0.318758	−	0.947836i	$-0.603266\pi$
$839$	−18.4660	−0.637517	−0.318758	+	0.947836i	$0.603266\pi$
$840$	10.8527	0.374454
$841$	−3.63156	−0.125226
$842$	30.9744	1.06745
$843$	−8.63128	−0.297277
$844$	−18.5783	−0.639493
$845$	0	0
$846$	−2.66603	−0.0916600
$847$	−35.9054	−1.23373
$848$	1.39814	0.0480124
$849$	24.3362	0.835216
$850$	−1.78138	−0.0611007
$851$	3.16743	0.108578
$852$	4.90919	0.168186
$853$	−9.77662	−0.334745	−0.167373	−	0.985894i	$-0.553528\pi$
$853$	−9.77662	−0.334745	−0.167373	+	0.985894i	$0.553528\pi$
$854$	27.2361	0.932002
$855$	−1.01713	−0.0347849
$856$	3.15753	0.107922
$857$	10.6732	0.364591	0.182296	−	0.983244i	$-0.441647\pi$
$857$	10.6732	0.364591	0.182296	+	0.983244i	$0.441647\pi$
$858$	0	0
$859$	−18.7484	−0.639686	−0.319843	−	0.947471i	$-0.603630\pi$
$859$	−18.7484	−0.639686	−0.319843	+	0.947471i	$0.603630\pi$
$860$	−16.0919	−0.548730
$861$	18.5074	0.630732
$862$	−24.3514	−0.829411
$863$	6.17773	0.210292	0.105146	−	0.994457i	$-0.466469\pi$
$863$	6.17773	0.210292	0.105146	+	0.994457i	$0.466469\pi$
$864$	−5.52753	−0.188050
$865$	48.0392	1.63338
$866$	14.6349	0.497315
$867$	−14.2663	−0.484510
$868$	15.0602	0.511177
$869$	0.385512	0.0130776
$870$	16.6930	0.565947
$871$	0	0
$872$	−6.28783	−0.212933
$873$	0.357907	0.0121133
$874$	−1.53315	−0.0518595
$875$	−38.5383	−1.30283
$876$	−18.8810	−0.637928
$877$	−12.0819	−0.407977	−0.203989	−	0.978973i	$-0.565391\pi$
$877$	−12.0819	−0.407977	−0.203989	+	0.978973i	$0.565391\pi$
$878$	31.3719	1.05875
$879$	−23.2147	−0.783014
$880$	−0.390862	−0.0131760
$881$	−1.09828	−0.0370019	−0.0185010	−	0.999829i	$-0.505889\pi$
$881$	−1.09828	−0.0370019	−0.0185010	+	0.999829i	$0.505889\pi$
$882$	−1.81121	−0.0609865
$883$	10.1705	0.342264	0.171132	−	0.985248i	$-0.445258\pi$
$883$	10.1705	0.342264	0.171132	+	0.985248i	$0.445258\pi$
$884$	0	0
$885$	−6.43502	−0.216311
$886$	−24.4634	−0.821863
$887$	−45.4387	−1.52568	−0.762841	−	0.646586i	$-0.776196\pi$
$887$	−45.4387	−1.52568	−0.762841	+	0.646586i	$0.776196\pi$
$888$	−3.27535	−0.109914
$889$	−65.4500	−2.19512
$890$	−19.2381	−0.644861
$891$	1.36556	0.0457479
$892$	−3.16144	−0.105853
$893$	5.47953	0.183365
$894$	22.8161	0.763086
$895$	−39.8743	−1.33285
$896$	3.27454	0.109395
$897$	0	0
$898$	−32.5272	−1.08545
$899$	23.1648	0.772589
$900$	0.306405	0.0102135
$901$	3.95488	0.131756
$902$	−0.666548	−0.0221936
$903$	−39.9614	−1.32983
$904$	10.2831	0.342010
$905$	2.57559	0.0856156
$906$	11.2856	0.374939
$907$	44.1186	1.46493	0.732467	−	0.680802i	$-0.238369\pi$
$907$	44.1186	1.46493	0.732467	+	0.680802i	$0.238369\pi$
$908$	−5.01391	−0.166393
$909$	−0.232072	−0.00769736
$910$	0	0
$911$	45.5440	1.50894	0.754470	−	0.656335i	$-0.227894\pi$
$911$	45.5440	1.50894	0.754470	+	0.656335i	$0.227894\pi$
$912$	1.58539	0.0524975
$913$	−2.46625	−0.0816210
$914$	−15.7954	−0.522464
$915$	27.5667	0.911325
$916$	−19.2863	−0.637238
$917$	−45.2182	−1.49324
$918$	−15.6355	−0.516050
$919$	−28.0857	−0.926461	−0.463230	−	0.886238i	$-0.653310\pi$
$919$	−28.0857	−0.926461	−0.463230	+	0.886238i	$0.653310\pi$
$920$	−3.20506	−0.105668
$921$	19.1779	0.631934
$922$	30.7808	1.01371
$923$	0	0
$924$	−0.970636	−0.0319316
$925$	1.30106	0.0427785
$926$	35.3937	1.16311
$927$	−6.87023	−0.225648
$928$	5.03671	0.165338
$929$	45.8989	1.50590	0.752948	−	0.658080i	$-0.228631\pi$
$929$	45.8989	1.50590	0.752948	+	0.658080i	$0.228631\pi$
$930$	15.2430	0.499837
$931$	3.72260	0.122003
$932$	−14.3970	−0.471590
$933$	−29.2836	−0.958703
$934$	−2.38161	−0.0779287
$935$	−1.10562	−0.0361576
$936$	0	0
$937$	−38.9093	−1.27111	−0.635555	−	0.772055i	$-0.719229\pi$
$937$	−38.9093	−1.27111	−0.635555	+	0.772055i	$0.719229\pi$
$938$	−3.83778	−0.125308
$939$	48.2995	1.57620
$940$	11.4550	0.373622
$941$	16.5652	0.540010	0.270005	−	0.962859i	$-0.412975\pi$
$941$	16.5652	0.540010	0.270005	+	0.962859i	$0.412975\pi$
$942$	9.15317	0.298226
$943$	−5.46568	−0.177987
$944$	−1.94161	−0.0631939
$945$	−37.8385	−1.23089
$946$	1.43922	0.0467929
$947$	−43.9435	−1.42797	−0.713986	−	0.700160i	$-0.753112\pi$
$947$	−43.9435	−1.42797	−0.713986	+	0.700160i	$0.753112\pi$
$948$	−3.26891	−0.106169
$949$	0	0
$950$	−0.629758	−0.0204320
$951$	−21.6522	−0.702120
$952$	9.26258	0.300202
$953$	−5.99352	−0.194149	−0.0970745	−	0.995277i	$-0.530949\pi$
$953$	−5.99352	−0.194149	−0.0970745	+	0.995277i	$0.530949\pi$
$954$	−0.680257	−0.0220241
$955$	53.7779	1.74021
$956$	−1.88105	−0.0608374
$957$	−1.49298	−0.0482611
$958$	26.1204	0.843913
$959$	−25.1171	−0.811074
$960$	3.31427	0.106968
$961$	−9.84743	−0.317659
$962$	0	0
$963$	−1.53627	−0.0495058
$964$	−5.22432	−0.168264
$965$	−9.59913	−0.309007
$966$	−7.95920	−0.256083
$967$	−37.2733	−1.19863	−0.599314	−	0.800514i	$-0.704560\pi$
$967$	−37.2733	−1.19863	−0.599314	+	0.800514i	$0.704560\pi$
$968$	−10.9650	−0.352430
$969$	4.48454	0.144064
$970$	−1.53780	−0.0493759
$971$	−3.56117	−0.114284	−0.0571418	−	0.998366i	$-0.518199\pi$
$971$	−3.56117	−0.114284	−0.0571418	+	0.998366i	$0.518199\pi$
$972$	5.00346	0.160486
$973$	32.9863	1.05749
$974$	−7.08808	−0.227117
$975$	0	0
$976$	8.31755	0.266238
$977$	−29.6645	−0.949052	−0.474526	−	0.880242i	$-0.657380\pi$
$977$	−29.6645	−0.949052	−0.474526	+	0.880242i	$0.657380\pi$
$978$	−20.4731	−0.654656
$979$	1.72060	0.0549905
$980$	7.78213	0.248591
$981$	3.05930	0.0976761
$982$	−1.18086	−0.0376828
$983$	−17.5706	−0.560416	−0.280208	−	0.959939i	$-0.590403\pi$
$983$	−17.5706	−0.560416	−0.280208	+	0.959939i	$0.590403\pi$
$984$	5.65192	0.180177
$985$	−43.3209	−1.38032
$986$	14.2472	0.453723
$987$	28.4465	0.905462
$988$	0	0
$989$	11.8015	0.375267
$990$	0.190171	0.00604404
$991$	47.3724	1.50483	0.752416	−	0.658688i	$-0.228888\pi$
$991$	47.3724	1.50483	0.752416	+	0.658688i	$0.228888\pi$
$992$	4.59919	0.146024
$993$	−25.8502	−0.820331
$994$	10.1397	0.321611
$995$	47.2070	1.49656
$996$	20.9123	0.662632
$997$	−31.0905	−0.984646	−0.492323	−	0.870413i	$-0.663852\pi$
$997$	−31.0905	−0.984646	−0.492323	+	0.870413i	$0.663852\pi$
$998$	−1.61241	−0.0510400
$999$	11.4197	0.361302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bn.1.11		14
13.2	odd	12		494.2.m.b.381.10	yes	28
13.7	odd	12		494.2.m.b.153.10	✓	28
13.12	even	2		6422.2.a.bm.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.10	✓	28	13.7	odd	12
494.2.m.b.381.10	yes	28	13.2	odd	12
6422.2.a.bm.1.11		14	13.12	even	2
6422.2.a.bn.1.11		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.58539 q^{3} +1.00000 q^{4} +2.09051 q^{5} +1.58539 q^{6} +3.27454 q^{7} +1.00000 q^{8} -0.486543 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.58539 q^{3} +1.00000 q^{4} +2.09051 q^{5} +1.58539 q^{6} +3.27454 q^{7} +1.00000 q^{8} -0.486543 q^{9} +2.09051 q^{10} -0.186969 q^{11} +1.58539 q^{12} +3.27454 q^{14} +3.31427 q^{15} +1.00000 q^{16} +2.82867 q^{17} -0.486543 q^{18} +1.00000 q^{19} +2.09051 q^{20} +5.19141 q^{21} -0.186969 q^{22} -1.53315 q^{23} +1.58539 q^{24} -0.629758 q^{25} -5.52753 q^{27} +3.27454 q^{28} +5.03671 q^{29} +3.31427 q^{30} +4.59919 q^{31} +1.00000 q^{32} -0.296419 q^{33} +2.82867 q^{34} +6.84546 q^{35} -0.486543 q^{36} -2.06596 q^{37} +1.00000 q^{38} +2.09051 q^{40} +3.56501 q^{41} +5.19141 q^{42} -7.69760 q^{43} -0.186969 q^{44} -1.01713 q^{45} -1.53315 q^{46} +5.47953 q^{47} +1.58539 q^{48} +3.72260 q^{49} -0.629758 q^{50} +4.48454 q^{51} +1.39814 q^{53} -5.52753 q^{54} -0.390862 q^{55} +3.27454 q^{56} +1.58539 q^{57} +5.03671 q^{58} -1.94161 q^{59} +3.31427 q^{60} +8.31755 q^{61} +4.59919 q^{62} -1.59320 q^{63} +1.00000 q^{64} -0.296419 q^{66} -1.17201 q^{67} +2.82867 q^{68} -2.43063 q^{69} +6.84546 q^{70} +3.09652 q^{71} -0.486543 q^{72} -11.9094 q^{73} -2.06596 q^{74} -0.998411 q^{75} +1.00000 q^{76} -0.612238 q^{77} -2.06190 q^{79} +2.09051 q^{80} -7.30364 q^{81} +3.56501 q^{82} +13.1907 q^{83} +5.19141 q^{84} +5.91337 q^{85} -7.69760 q^{86} +7.98514 q^{87} -0.186969 q^{88} -9.20255 q^{89} -1.01713 q^{90} -1.53315 q^{92} +7.29151 q^{93} +5.47953 q^{94} +2.09051 q^{95} +1.58539 q^{96} -0.735611 q^{97} +3.72260 q^{98} +0.0909688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * q^99

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